Weak Bi-Center and Bifurcation of Critical Periods in a Three-Dimensional Symmetric Quadratic System

This paper focuses on the weak bi-center and bifurcation of critical periods in a class of three-dimensional quadratic systems with a special type of symmetry. Center manifold theory is applied to prove that the system admits either a rough bi-center or a weak bi-center of infinite order (i.e. isochronous hi-center) rather than a weak hi-center of finite order. As a consequence, no bifurcation of critical periods can be generated from the bi-center.